ASYMPTOTIC BEHAVIOR OF THE NONLINEAR VLASOV EQUATION WITH A SELF-CONSISTENT FORCE

被引:6
作者
Choi, Sun-Ho [1 ]
Ha, Seung-Yeal [1 ]
机构
[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea
基金
新加坡国家研究基金会;
关键词
asymptotic completeness; self-consistent Vlasov equation; phase transition; long-ranged force; short-ranged force; scattering; DEFINED SCATTERING OPERATORS; KLEIN-GORDON EQUATIONS; POISSON SYSTEM; GLOBAL EXISTENCE; DIMENSIONS; INITIAL DATA; SPACE; PARTICLES;
D O I
10.1137/100815098
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a critical threshold phenomenon on the L-1-asymptotic completeness for the nonlinear Vlasov equation with a self-consistent force. For a long-ranged self-consistent force, we show that the nonlinear Vlasov equation has no L-1-asymptotic completeness, which means that the nonlinear Vlasov flow cannot be approximated by the corresponding free flow in L-1-norm time-asymptotically. In contrast, for a short-ranged force, the nonlinear Vlasov flow can be approximated by the free flow time-asymptotically. Our result corresponds to the kinetic analogue of scattering results to the Schrodinger-type equations in quantum mechanics.
引用
收藏
页码:2050 / 2077
页数:28
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